Being affected by surrounding buildings, objects, pedestrians, vehicles and the ground, etc, a wireless signal may suffer reflection, refraction, diffraction and dispersion, etc. Therefore, the wireless signal received by the receiving end generally has suffered severe fading and time delay spread. In order to recover the transmitted data, the receiver needs to estimate the wireless channel gone through by the signal and then to compensate for the loss suffered by the received signal. The module for estimating the channel is referred to as a channel estimation module, and the module for compensating for the received signal is referred to as an equalization module. The channel estimation module is essential to the wireless system. The better the performance of the channel estimation is, the better the bit error performance of the system will be, that is, the more data the system will correctly receive.
Orthogonal Frequency Division Multiplexing (OFDM) technology is a transmission technology newly developing in recent years. The OFDM system first performs IFFT (Inverse Fast Fourier Transform) transform to data to be transmitted at the transmitting end to transform it into a time signal which is subsequently transmitted in time domain. At the receiving end, the received signal first is transformed into frequency domain through FFT (Fast Fourier Transform), and then undergoes such operations as equalization, demodulation and decoding to restore the transmitted signal. Since a multipath channel with certain time delay extension gone through by the transmitted signal in time domain will be equivalently transformed to a flat fading channel, the OFDM system has great anti-fading capability, and has been widely used in recent years, for example, wireless communication systems such as Wimax (Worldwide Interoperability for Microwave Access) system and LTE (Long Term Evolution), and digital television broadcasting systems such as DMB-T (Digital Multimedia Broadcast-Terrestrial), CMMB (China Mobile Multimedia Broadcasting) and DVB (Digital Video Broadcasting).
Herein, the frequency domain data carried by the kth subcarrier in the lth OFDM symbol is Xk,l, and the frequency domain equivalent received signal Yk,l, corresponding to the frequency domain data may be expressed as:Yk,l=Hk,lXk,l+Nk,l  (1)wherein, k and l are integrals, Hk,l is the equivalent frequency domain flat fading channel gone through by Xk,l, Nk,l is the frequency domain equivalent additive Gaussian white noise of which the average is zero and the variance is σN2.
The channel estimation for the OFDM system is an estimation of the equivalent frequency domain channel response Hk,l. Minimum Mean Square Error (MMSE) criterion is a criterion minimizing the estimation error average. The channel estimation algorithm based on MMSE criterion is one of the optimal channel estimation algorithms. According to the MMSE channel estimation algorithm, the estimation value Ĥk,l of the channel frequency domain response at the kth subcarrier in the lth OFDM symbol may be calculated according to formula (2):Ĥk,l=wk,lHĤk,lP  (2)
In the above formula, the variable Ĥk,l is an estimation value of the channel frequency domain response at the subcarrier (k,l), the vector wk,l is a filter coefficient of the MMSE channel estimator, the vector Ĥk,lP is formed by arrangement of channel impulse response evaluation values of pre-selected pilot points for estimating the channel frequency domain response at the subcarrier (k,l). Assuming that each data subcarrier performs the MMSE channel estimation using M observation points, M being an integral, and the serial number for the M observation points respectively being (k1, l1), (k2, l2), . . . , (kM, lM), then the vector Ĥk,lP may be expressed as the following formula (3):Ĥk,lP=└Ĥk1,l1 Ĥk2,l2 . . . ĤkM,lM┘  (3)
According to MMSE criterion, wk,l is a solution minimizing the function J(wk,l), wherein the function J(wk,l) is given by formula (4):J(wk,l)=E{∥Ĥk,l−Hk,l∥2}  (4)Wherein, the function E{ } is used for calculating the mathematical expectation value.
According to the Orthogonal principle, wk,l may be calculated through the following formula (5).wk,l=θk,lTΦk,l−1  (5)
Wherein, θk,l is a cross-correlation vector for the frequency domain channel response at the subcarrier (k,l) and the M observation points received value, which can be expressed as:θk,l=[θk-k1,l-l1 θk-k2,l-l2 . . . θk-kM,l−lM]T  (6)
The correlation value θk-km,l-lm, M=1, 2, . . . , M in formula (6) may be expressed as follows:θk-km,l-lm=E{Hk,l·Ĥ*km,lm}  (7)
In formula (5), matrix Φk,l is a self-correlation matrix of the M observation points received value, which may be expressed as follows:
                              Φ                      k            ,            l                          =                  [                                                                      Φ                                                                                    k                        1                                            -                                              k                        1                                                              ,                                                                  l                        1                                            -                                              l                        1                                                                                                                                          Φ                                                                                    k                        2                                            -                                              k                        1                                                              ,                                                                  l                        2                                            -                                              l                        1                                                                                                                        …                                                              Φ                                                                                    k                        M                                            -                                              k                        1                                                              ,                                                                  l                        M                                            -                                              l                        1                                                                                                                                                                  Φ                                                                                    k                        1                                            -                                              k                        2                                                              ,                                                                  l                        1                                            -                                              l                        2                                                                                                                                          Φ                                                                                    k                        2                                            -                                              k                        2                                                              ,                                                                  l                        2                                            -                                              l                        2                                                                                                                                                                                                                        Φ                                                                                    k                        M                                            -                                              k                        2                                                              ,                                                                  l                        M                                            -                                              l                        2                                                                                                                                                ⋮                                                                                                                          ⋱                                                                                                                                                                    Φ                                                                                    k                        1                                            -                                              k                        M                                                              ,                                                                  l                        1                                            -                                              l                        M                                                                                                                                          Φ                                                                                    k                        2                                            -                                              k                        M                                                              ,                                                                  l                        2                                            -                                              l                        M                                                                                                                        …                                                              Φ                                                                                    k                        M                                            -                                              k                        M                                                              ,                                                                  l                        M                                            -                                              l                        M                                                                                                                          ]                                    (        8        )            
Wherein, the self-correlation value Φkm-km′,lm-lm′, ∀m′,m=1, 2, . . . , M may be expressed as follows:Φkm-km′,lm-lm′=E{Ĥkm,lm·Ĥ*km′,lm′}  (9)
The correlation value given by formula (7) and (9) includes both time domain correlation and frequency domain correlation. Generally, it may be considered that the time domain correlation and the frequency domain correlation in the correlation values are independent from each other, therefore formula (7) and (9) may respectively be expressed as a product of the time domain correlation value and the frequency domain correlation value, as shown by following formula (10) and (11).
                                              ⁢                              θ                                          k                -                                  k                  m                                            ,                              l                -                                  l                  m                                                              =                                                    θ                                  Δ                  ⁢                                                                          ⁢                  f                                            ⁡                              (                                  k                  -                                      k                    m                                                  )                                      ·                                          θ                                  Δ                  ⁢                                                                          ⁢                  t                                            ⁡                              (                                  l                  -                                      l                    m                                                  )                                                                        (        10        )                                          θ                                                    k                m                            -                              k                                  m                  ′                                                      ,                                          l                m                            -                              l                                  m                  ′                                                                    =                                                            N                0                            ⁢                              δ                ⁡                                  (                                                                                    k                        m                                            -                                              k                                                  m                          ′                                                                                      ,                                                                  l                        m                                            -                                              l                                                  m                          ′                                                                                                      )                                                                                    E                s                            ⁡                              (                                                      k                    m                                    ,                                      l                    m                                                  )                                              +                                                    θ                                  Δ                  ⁢                                                                          ⁢                  f                                            ⁡                              (                                                      k                    m                                    ,                                      k                                          m                      ′                                                                      )                                      ·                                          θ                                  Δ                  ⁢                                                                          ⁢                  t                                            ⁡                              (                                                      l                    m                                    -                                      l                                          m                      ′                                                                      )                                                                        (        11        )            Wherein, N0 is a single side band power spectral density, N0=2σN2, Es(km,lm) is the energy of the transmitted signal carried by the subcarrier (km,lm). The function δ(km−km′,lm−lm′) is expressed as follows.
                              δ          ⁡                      (                                                            k                  m                                -                                  k                                      m                    ′                                                              ,                                                l                  m                                -                                  l                                      m                    ′                                                                        )                          =                  {                                                    1                                                                                  if                    ⁢                                                                                  ⁢                                          k                      m                                                        =                                                                                    k                                                  m                          ′                                                                    ⁢                                                                                          ⁢                      and                      ⁢                                                                                          ⁢                                              l                        m                                                              =                                          l                                              m                        ′                                                                                                                                                0                                            others                                                                        (        12        )            
It can be seen from the above analysis that the already known time domain correlation value θΔt(l−lm) and the frequency domain correlation value θΔf(k−km) are the premise for a smooth implementation of the MMSE channel estimation algorithm.
Wherein, the time domain correlation θΔt(l−lm) is correlated with a relative moving speed of the transmitting end and the receiving end and the type of Doppler fading experienced by the channel. For example, when the Doppler power spectral of the channel is the most common Clarke model (also referred to as Jakes model), the time domain correlation value θΔt(l−lm) may be expressed as follows:θΔt(l−lm=J0(2πfdTs(l−lm))  (13)Wherein, function J0 is the first kind of zero order Bessel function, Ts is the baseband sample period of the system, fd is a single base band maximum Doppler frequency, which is correlated with the relative moving speed of the transmitting end and the receiving end, and can be calculated through the following formula (14):
                              f          d                =                                            F              G                        ·            v                    c                                    (        14        )            
In formula (14), FG is a carrier frequency, v is a moving speed of the receiving end relative to the transmitting end, c is the light speed. In other words, under the premise that the type of channel Doppler is known, as long as the moving speed of the receiving end relative to the transmitting end is estimated and obtained, the time domain correlation characteristic of the channel may be obtained.
However, compared to the calculating process for the time domain correlation, the calculating process for the frequency domain correlation characteristic of the channel is more complicated. This is because the frequency domain correlation characteristic of the channel is related with the path number of the time multipath channel through which the signal is transmitted, power of each path and a time delay. The algorithm for calculating frequency domain correlation is generally divided into two categories: one is to estimate the time multipath channel through which the signal is transmitted, the other is to take statistics on the frequency domain received pilot signal based on the definition of channel frequency domain correlation, to obtain the estimation value of the channel frequency domain correlation.
In recent communication systems applying OFDM principle, the pilot usable for channel estimation may be limited, such as TD-LTE system with UE-Specific Reference Signal. In such a case, a small piece of time-frequency transmission resource used by certain receiver may have been transmitted through a channel different from time-frequency transmission resources around it. That is, the receiver faces two serious problems: firstly, it is impossible for it to observer how the multipath channel experienced by it is distributed in the whole frequency band; secondly, the number of the pilot usable by it is very limited. The first problem makes the receiver unable to estimate the time domain multipath channel through which the received signal is transmitted. The second problem makes the receiver unable to accurately estimate the channel frequency domain correlation coefficient required by all MMSE channel estimation using frequency receiving pilot.